lab 6 propagated uncertainty in measuremensts

Purpose: to find density of different cylinders along with the propagated error.

At the beginning of class we received three cylinders which were made up of copper steel and aluminum. We were instructed to solve for the density of the volume. 

The Picture above shows the three cylinders (steel,copper and aluminum). Along with the cylinders there is a vernier caliper (that fancy tool at the bottom)which is a tool that we used to measure the height and diameter of the cylinders.

Here is a picture showing how we measured the height.

A scale was used to get the mass of all three objects. 

The picture below  shows the measurements of all three objects.

We took the data from the table above and solved for the density of copper steel and aluminum.

After we solved for the density we had to solve for the propagated error of our calculated density.

We solved for density of all cylinders by using the the equation D=M/V M=mass,V=volume.

Which turned out to be D= M/Pi*(r^2)*h.

We also had to solve for propagated error of density by taking partial derivatives of the radius, height and mass.

The equation came out to be following dd= (1/Pi*(r^2)*h)*DeltaM + (M/Pi*(2r)*h)*DeltaR + (M/Pi*(r^2)*1)*DeltaH.

For Part two of the lab we had to figure out the mass of the hanging object.

Here is a picture of the initial hanging mass.

As you are able to visualize there is a newton measuring device attached to each side of the hanging mass.

The one to the left read 5 N + or - .25 N and the one to the right read 6.75 N + or - .25 N.

After we recorded the newton readings we had to measure the angle of the strings with this clever device on the left.

Here is a picture of when we measured the angle.

Here is another picture of the lab set up.

After we had all of our data we set up an equation to find the mass of the hanging object by taking the components of Y of both the strings. The equations came out to be Mass= (F1sin26+F2sin40)/g, g is the acceleration due to gravity.

F1 = 5 N +or- .25 N @ 26 degrees  +or- 2

F2 = 6.75 +or- .25 N @ 40 degrees  +or- 2

We derived our propagated error at the bottom, by taking partial derivatives of the forces

 and angles of the angles and forces we measured. Since calculus does not recognize degrees we had to switch our degrees to radians.

We repeated the previous steps for other hanging masses and turned them in at the end of class.